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There are 10 two color combinations for land in magic. Black-white, black-blue, black-green, etc. For any one color, 4 of those 10 will contain that color. I.e. four of these two color combinations contain black. That's almost half.

My question, then, is why not run a rainbow (5 color) deck with twenty dual color lands, two from each color permutation? I assume for the sake of simplicity a 20 land 40 non-land split but the principal is the same.

One of the arguments against rainbow decks is that you can easily find yourself in a position where you don't have the land you need. But in this construction, 40 percent of lands will give you any single color, which seems pretty good to me. Am I missing something?

That's assuming that you are only using mono-color cards in your rainbow deck, which (as far as I can tell) removes many of the benefits of running a rainbow deck. Multicolored cards tend to be stronger than single-colored cards with the same cost. A well-constructed rainbow deck lets you use lots of multicolored cards.
– BJ MyersNov 30 '17 at 22:21

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You answered your own question: "[Y]ou can easily find yourself in a position where you don't have the land you need."
– RainboltDec 1 '17 at 1:50

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I know a lot of experienced Magic players probably think the answer here is really obvious, but let's not confuse that with "unclear" or "too broad". The core reasons that 5-color decks tend to be iffy are really pretty objective.
– Cascabel♦Dec 1 '17 at 2:22

1 Answer
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Playing multi-color decks is desirable because it lets you make a powerful and versatile deck by cherrypicking the best cards (for your strategy) from multiple colors.

So, why are 4- and 5- color decks so comparatively rare?

A lot of the strongest spells of a color have deeper mana requirements.

Make a list of your favorite powerful cards. A lot of them probably have costs like 2WW rather than 3W, huh? This drastically alters the math of consistent color access. If you look at this number-crunching article by Frank Karsten, you'll see he figures 12 sources are enough to consistently cast a 2C-cost spell on turn 3, but you need 19 sources to get the same quality of access to a 1CC-cost spell on turn 3. 19!

This is an active, purposeful design decision to make these cards easier to cast on-curve and on-time in a deck that's dedicated to those colors, and harder to include in a deck that only splashes a color.

Cards are strongest when you play them on time. A mana base that's heavy on comes-into-play-tapped lands or requires casting land-selection spells like Borderland Ranger to set up your mana introduces notable lag before you can start playing spells that will really interact with your opponent.

Opponents can disrupt your mana base. Consider how much tighter mana requirements become when you're playing against a deck with 2x Rishadan Port and 4x Wasteland.

All these serve as a damper on the greediest multi-color decks. On top of that, because:

The color's "pie slices" overlap (e.g. green or white can both play effective enchantment removal, so you only need one of those colors to get that ability in your deck).

Not every color in a format will meaningfully support the specific synergies / strategies you're trying to exploit. (Maybe there just are no red cards worth playing in your midrange deck, even with perfect mana.)

A stable 5-color manabase can lock you out of playing amazing utility lands like Academy Ruins.

— there's often very little to gain from building a full four- or five- color deck instead of one that's "just" three colors.

Another way to look at this is to look through current competitive decks, for example, vintage, legacy, and modern on MTGGoldfish. You'll tend to notice that 5-color or even 4-color decks are most common in vintage and legacy (with no-drawback original dual lands), and especially in modern, they often have to do interesting things to actually get all those colors easily enough to make the deck work.
– Cascabel♦Dec 1 '17 at 2:20